mensuration area volumes Model Questions & Answers, Practice Test for ssc chsl tier 1 2023
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Mensuration: Area & Volumes
A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form of a square, then its area will be:
Answer: (a)
Length of wire = 2π × R = $(2 × {22}/{7} × 56)$cm = 352 cm.
Side of the square = ${352}/4$ cm = 88 cm.
Area of the square = (88 × 88) $cm^2 = 7744 cm^2$.
The diameter of circle with centre at C is 50 cm. CP is a radial segment of the circle. AB is a chord perpendicular to CP and passes through P. CP produced intersects the circle at D. If DP = 18 cm then what is the length of AB?
Answer: (d)
In ΔACP, CP = CD – PD = 25 – 18 = 7
By Pythagoras theorem
$AC^2 = CP^2 + AP^2$
AP = $√{AC^2 - CP^2} = √{(25)^2 - (7)^2}$
= $√{625 - 49} = √{576}$ = 24cm
Similarly, PB = 24 cm
∴ AB = AP + PB
= 24 + 24 = 48 cm
A wall is of the form of a trapezium with height 4 m and parallel sides being 3 m and 5 m. What is the cost of painting the wall, if the rate of painting is Rs. 25 per sq m?
Answer: (c)
∵ Area of trapezium = $1/2 (3 + 5) × 4 = 16 m^2$
∴ Total cost of painting Rs.25 per sq m = 16 × 25 = Rs.400
The sides of a triangle are 50 m, 40 m and 30 m. What is the length of the altitude of the vertex opposite to the side 50 m long?
Answer: (c)
Let a = 30 m, b = 40 m and c = 50 m
Now, 2s = 30 + 40 + 50
⇒ s = 60 m
∴ Δ = $√{60(60 - 30)(60 - 40)(60 - 50)}$
= $√{60 × 30 × 20 × 10}$ = 600
⇒ $1/2 × AB × CD = 600 ⇒ CD = {600 × 2}/{50}$ = 24m
ABCD is a parallelogram where AC and BD are the diagonals. If ∠BAD = 60°, ∠ADB = 90°, then what is $BD^2$ equal to ?
Answer: (c)
${BD}/{AB} = {√3x}/{2x} = √3/2$
⇒ $BD^2 = 3/4 AB^2$
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